where \(GP\)  stands for the gradient penalty term (see detailed form in [1]}) and \(\lambda \)  is its corresponding weight. This loss aims at maximizing the critic output for real normal data \(\mathbf {x}_j\) 's, meanwhile minimizing the critic output for estimated normal data \(G_1(E(\mathbf {x}_i))\) 's from the generator \(G_1\) . Higher output indicates that the input to the critic is more realistic. On the other hand, as part of the well-known alternative GAN training strategy, the generator \(G_1\)  together with the encoder \(E\)  can be trained by minimizing the adversarial loss \(L_a\) ,
\(L_a = - \frac{1}{N}\sum _{i=1}^N D(G_1(E(\mathbf {x}_i))) \,\) 
